Finite Group Databasebeta

← #67×C9⋊C9 #14517413

Subgroups — #67×C9⋊C9 #14517413

Order 1944.

412 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C9⋊C9C211yesmaximal, characteristic, complemented
2C2×D3×C9⋊C9C211yesmaximal, characteristic, complemented
3Dic3×C9⋊C9C211yesmaximal, characteristic, complemented
4C3×C9×#67C313yesmaximal
5C3×C9×#67C311yesmaximal, characteristic
6D4×C9⋊C9—31nomaximal
7C2×C3×C9⋊C9—21no—
8C2×C3×C9⋊C9C2211yescharacteristic
9D3×C9⋊C9—21no—
10C22×C32×C9C2×C311yescharacteristic
11C22×C32×C9C2×C313yes—
12C2×C3×D3×C9C2×C313yes—
13C2×C3×D3×C9C2×C311yescharacteristic
14C3×C9×Dic3C2×C313yes—
15C3×C9×Dic3C2×C311yescharacteristic
16C22×C9⋊C9—23no—
17C22×C9⋊C9—21no—
18C22×C9⋊C9—31no—
19C22×C9⋊C9D311yescharacteristic, complemented
20C4×C9⋊C9—31no—
21C3×C9⋊C9D411yescharacteristic, complemented, Sylow
22C32×#67C3211yescharacteristic
23C3×D4×C9—31no—
24C3×D4×C9—33no—
25C9×#67—33no—
26C9×#67C913yescomplemented
27C2×C32×C9—21no—
28C2×C32×C9—23no—
29C2×C32×C9C22×C311yescharacteristic
30C2×C32×C9C22×C313yes—
31C3×D3×C9—21no—
32C3×D3×C9—23no—
33C2×C9⋊C9—26no—
34C2×C9⋊C9—22no—
35C2×C9⋊C9—21no—
36C2×C9⋊C9—23no—
37C2×C9⋊C9—21no—
38C2×C9⋊C9—61no—
39C2×C9⋊C9C2×D311yescharacteristic
40C22×C33C2×C3211yescharacteristic
41C2×C32×D3C2×C3211yescharacteristic
42C32×Dic3C2×C3211yescharacteristic
43C22×C3×C9—21no—
44C22×C3×C9—23no—
45C22×C3×C9—23no—
46C22×C3×C9—33no—
47C22×C3×C9—31no—
48C22×C3×C9—33no—
49C22×C3×C9—63no—
50C22×C3×C9C2×C913yescomplemented
51C22×C3×C9C3×D313yes—
52C22×C3×C9C3×D311yescharacteristic
53C2×D3×C9—33no—
54C2×D3×C9C2×C913yescomplemented
55C3×C4×C9—31no—
56C3×C4×C9—33no—
57C9×Dic3—33no—
58C9×Dic3C2×C913yescomplemented
59C32×C9C3×D411yescharacteristic
60C32×C9C3×D413yes—
61C9⋊C9—23no—
62C9⋊C9—21no—
63C9⋊C9#6711yescharacteristic, direct product factor
64C32×D4—31no—
65C3×#67C3×C911yescharacteristic
66C3×#673−1+213yes—
67D4×C9—33no—
68D4×C9—93no—
69C2×C33—21no—
70C2×C33C22×C3211yescharacteristic
71C32×D3—21no—
72C2×C3×C9—22no—
73C2×C3×C9—26no—
74C2×C3×C9—23no—
75C2×C3×C9—21no—
76C2×C3×C9—21no—
77C2×C3×C9—23no—
78C2×C3×C9—26no—
79C2×C3×C9—23no—
80C2×C3×C9—23no—
81C2×C3×C9—33no—
82C2×C3×C9—63no—
83C2×C3×C9—63no—
84C2×C3×C9—66no—
85C2×C3×C9—61no—
86C2×C3×C9—63no—
87C2×C3×C9C22×C913yes—
88C2×C3×C9C2×C3×D313yes—
89C2×C3×C9C2×C3×D311yescharacteristic
90D3×C9—23no—
91D3×C9—63no—
92C22×C32—21no—
93C22×C32—23no—
94C22×C32—31no—
95C22×C32C2×C3×C911yescharacteristic
96C22×C32C2×3−1+213yes—
97C22×C32C32×D311yescharacteristic
98C2×C3×D3C2×C3×C911yescharacteristic
99C2×C3×D3C2×3−1+213yes—
100C32×C4—31no—
101C3×Dic3C2×C3×C911yescharacteristic
102C3×Dic3C2×3−1+213yes—
103C22×C9—23no—
104C22×C9—33no—
105C22×C9—33no—
106C22×C9—63no—
107C22×C9—93no—
108C22×C9D3×C913yescomplemented
109C4×C9—33no—
110C4×C9—93no—
111C33C32×D411yescharacteristic
112C3×C9—21no—
113C3×C9—23no—
114C3×C9—23no—
115C3×C9—33no—
116C3×C9—63no—
117C3×C9D4×C913yescomplemented
118C3×C9C3×#6713yes—
119C3×C9C3×#6711yescharacteristic
120C3×D4—31no—
121C3×D4—33no—
122#67C9⋊C911yescharacteristic, direct product factor
123C2×C32—22no—
124C2×C32—26no—
125C2×C32—21no—
126C2×C32—23no—
127C2×C32—21no—
128C2×C32—21no—
129C2×C32—23no—
130C2×C32—61no—
131C2×C32C22×C3×C911yescharacteristic
132C2×C32C22×3−1+213yes—
133C2×C32C2×C32×D311yescharacteristic
134C3×D3—21no—
135C3×D3—23no—
136C2×C9—26no—
137C2×C9—23no—
138C2×C9—23no—
139C2×C9—33no—
140C2×C9—63no—
141C2×C9—66no—
142C2×C9—63no—
143C2×C9—63no—
144C2×C9—183no—
145C2×C9C2×D3×C913yes—
146C22×C3—21no—
147C22×C3—23no—
148C22×C3—31no—
149C22×C3—33no—
150C22×C3C2×C9⋊C911yescharacteristic, complemented
151C22×C3C3×D3×C911yescharacteristic
152C22×C3D3×3−1+213yes—
153C2×D3C2×C9⋊C911yescharacteristic, complemented
154C3×C4—31no—
155C3×C4—33no—
156Dic3C2×C9⋊C911yescharacteristic, complemented
157C32—21no—
158C32—23no—
159C32C3×D4×C911yescharacteristic
160C32D4×3−1+213yes—
161C32C32×#6711yescharacteristic
162C9—23no—
163C9—33no—
164C9—63no—
165C9C9×#6713yescomplemented
166D4—31noSylow
167C2×C3—22no—
168C2×C3—26no—
169C2×C3—21no—
170C2×C3—23no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—23no—
174C2×C3—61no—
175C2×C3—63no—
176C2×C3C22×C9⋊C911yescharacteristic
177C2×C3C2×C3×D3×C911yescharacteristic
178C2×C3C2×D3×3−1+213yes—
179D3—21no—
180C22—31no—
181C22D3×C9⋊C911yescharacteristic, complemented
182C4—31no—
183C3—21no—
184C3—23no—
185C3D4×C9⋊C911yescharacteristic, complemented
186C3C3×C9×#6711yescharacteristic
187C3#67×3−1+213yes—
188C2—21no—
189C2—61no—
190C2C2×D3×C9⋊C911yescharacteristic
subgroupG/H
center, FrattiniC2×C32C2×C32×D3
commutatorC2×C32C22×C3×C9
FittingC22×C3×C9⋊C9C2
socle, cosocleC2×C33C22×C32
prime radicalC32×#67C32
hypercenterC22×C9⋊C9D3
hypocenterC3D4×C9⋊C9
LCSG ▷ C2×C32 ▷ C3
UCSC1 ◁ C2×C32 ◁ C22×C9⋊C9

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×C9⋊C9C2semidirect
2. C2×D3×C9⋊C9C2semidirect
3. Dic3×C9⋊C9C2semidirect
19. C22×C9⋊C9D3semidirect
21. C3×C9⋊C9D4semidirect
26. C9×#67C9semidirect
50. C22×C3×C9C2×C9semidirect
54. C2×D3×C9C2×C9semidirect
58. C9×Dic3C2×C9semidirect
63. C9⋊C9#67direct (N × H)
108. C22×C9D3×C9semidirect
117. C3×C9D4×C9semidirect
122. #67C9⋊C9direct (N × H)
150. C22×C3C2×C9⋊C9semidirect
153. C2×D3C2×C9⋊C9semidirect
156. Dic3C2×C9⋊C9semidirect
165. C9C9×#67semidirect
181. C22D3×C9⋊C9semidirect
185. C3D4×C9⋊C9semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C9⋊C92
C2×D3×C9⋊C92
Dic3×C9⋊C92
C3×C9×#673
D4×C9⋊C93